Suppose we want a satellite to revolve around the earth 5 times a day.What should be the radius of its orbit? (The mass of the earth is 5.97 × 10²⁴ kg,G = 6.67 × 10^-11 N ∙ m²/kg²,and you can neglect the presence of the moon.) A)1.44 × 10⁷ m B)0.690 × 10⁷ m C)7.22 × 10⁷ m D)2.11 × 10⁷ m

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Quizplus · Accepted Answer

To find the radius of the orbit for a satellite to revolve around the Earth 5 times a day, we use the formula for the orbital period $T$ of a satellite: $T = 2\pi\sqrt{\frac{r^3}{GM}}$, where $r$ is the radius of the orbit, $G$ is the gravitational constant, and $M$ is the mass of the Earth. Rearranging the formula to solve for $r$, and knowing that the satellite revolves around the Earth 5 times a day (which means $T = \frac{24}{5}$ hours or $T = \frac{24 \times 3600}{5}$ seconds for one revolution), we can plug in the values for $G$ and $M$ to find $r$. The calculation involves solving for $r$ in the equation given the values for $T$, $G$, and $M$, leading to the correct radius for the desired orbital period. The exact calculation requires substituting the numerical values and solving for $r$, which results in the radius closest to the option A) $1.44 \times 10^{7} m$.

Suppose We Want a Satellite to Revolve Around the Earth